1. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 1 Abstract Data Types Motivation Abstract Data Types Example Using math. functions to describe an ADT's operations.

2. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 2 Motivation for ADTs To organize some data, we need to say what general form it has, and what we expect to do with it. Object-oriented programming provides one way of organizing data: using classes, with their data members and methods. It is often helpful to specify our data without having to choose the particular data structure yet.

3. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 3 Abstract Data Type (Def.) An abstract data type consists of two parts: a description of the general form of some data. a set of methods. The data is usually a set of elements, but may also include relationships among the elements. { 2, 3, 5, 7, 11} [2 < 3, 3 < 5, 5 < 7, 7 < 11, etc.]

4. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 4 ADT Methods Each method in an ADT names and specifies an operation. The operation can be described by a function. Normally, an instance of the ADT data is one of the arguments to the function. Examples of methods: INSERT(x) MEMBER(x) SMALLEST( ) CREATE( ) --- A "constructor" does not use an instance of the ADT, but creates one.

5. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 5 Example ADT: Stack of Integers Data: (Ordered) list of integers. Methods: CREATE, PUSH, POP, TOP, DESTROY

6. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 6 Using Math. Functions to Describe ADT Methods Why? Math. can be used to give a concise and unambiguous description of a method. What? 1. gives a clear indication of input & output. 2. clarifies how the data changes and what is returned by the operation.

7. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 7 Math. Description of Methods: Domain and Range of the Method's function Example: the POP operation on a stack can be described by a mathematical function: f POP : stacks  elements  stacks stacks = the set of all possible stacks (according to this ADT). elements = the set of all acceptable elements in our stacks (e.g., integers). Because the operation produces an element and it causes a change to the stack, the range of f POP is a cartesian product.

8. CSE 373, Copyright S. Tanimoto, 2002 Abstract Data Types - 8 The Function's Effect Now we describe how the function changes the stack and produces a value. f POP : [e 0,e 1,...,e n-1 ] |  ( e n-1, [e 0,e 1,...,e n-2 ] ) The symbol " |  " means "maps to". On its left side is a description of a generic domain element. On its right side is a description of the corresponding range element. This formula indicates that the POP operation takes an n- element stack, returns the last element, and removes it from the stack.